I have some similar reports setup, that I want to trigger on the first of the month but run for the previous month. See an example of my settings below.
Report start is "1 month ago" and the report end is "now" - then you just schedule it to run the 1st of every month. I set mine to run at 12:01am on the 1st of the month. The "desired start time" just needs to be a day in the past, but the time is whatever time you want it to start on that 1st day of the month. (But I do 12:01am, since the "report end" is set to "now" which causes the report to run up to 12:01am of the 1st of the month - which captures the 'previous month')
Hope this helps and makes sense.
When I view my generated reports, I can see my report start and end dates/times look correct - its getting the "previous month."